Export srs_diff_est()

[vinniott]

Fixes #333

Note:

• There is no @example yet because I did not have time yet to get fully familiar with the whole package.
• I updated NEWS.md as suggested in CONTRIBUTING.md but I am not sure whether I did that correctly.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.78%. Comparing base (7eafeb8) to head (5d476b5).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #340   +/-   ##
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  Coverage   92.78%   92.78%           
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  Files          31       31           
  Lines        2992     2992           
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  Hits         2776     2776           
  Misses        216      216           

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[jgabry]

Thank you @vinniott.

There is no @example yet because I did not have time yet to get fully familiar with the whole package.

@avehtari or @MansMeg, is there any specific example you'd like to use for this in the documentation?

[avehtari]

The example should be based on flexible enough model so that elpd(log_lik_matrix) and loo(log_lik_matrix) differ more than by 1. The current example_loglik_matrix() has too few observations. The example used in tests for subsampling is one parameter model. Should we have a real model, or store another example loglik matrix?

After we have useful loglik matrix, the example code would be something like

# Use posterior predictive density as the fast but biased method for all observations
lpd <- elpd(log_lik_matrix)
sum(lpd$pointwise[,"elpd"])

# Use PSIS-LOO for subsample of 50 randomly selected observations
idx <- sample(1:N, 50)
elpd_loo_sub <- loo(log_lik_matrix[,idx])
20 * sum(elpd_loo_sub$pointwise[,"elpd_loo"])

# Use difference estimator to combine fast result and subsampled accurate result
loo:::srs_diff_est(lpd$pointwise[,"elpd"], elpd_loo_sub$pointwise[,"elpd_loo"], idx)

# Comparison to using PSIS-LOO for all observations
loo(log_lik_matrix)

This matches what someone was asking

[jgabry]

Should we have a real model, or store another example loglik matrix?

Either is fine by me. Also if we're only using it for this example, we could also just generate an example loglik matrix in the example code instead of storing it.